Initially I started to work on exact solutions of the Einstein field equations, especially spherically symmetric solutions. I analysed the effects of the cosmological constant on such systems and thereby developed an interest in the cosmological constant and the dark energy problem. I analysed various dark matter models in the context of classical gravity, brane world models and Bose-Einstein condensates, and also worked in modified gravity. I was always intrigued by generalisations of general relativity where the manifold underlying the theory is for instance allowed to carry torsion as well as curvature, Einstein-Cartan theory. In recent year I have also worked on the eigenspinors of the charge conjugation operator which I named dark spinors in spring 2008. The dynamical behaviour of these dark spinors in cosmology is very similar to that of scalar fields. However, due to their more complicated and hence more interesting mathematical structure, some differences are present. I could for example show that the theory of dark spinor inflation yields predictions very similar to scalar field inflation with a few nice extra properties on top. In addition to my mathematical and theoretical physics research I am also working in one particular area of pure mathematics, namely the analysis of partial differential equations. In particular I am interested in the rigorous analysis of PDEs in micropolar or Cosserat elasticity. This theory in general yield non-linear PDEs and currently I am identifying appropriate function spaces and establishing a priori estimates for solutions.